Did you ever find yourself in a situation during a math or physics class
where you just couldn't understand a single word coming out of your teacher's mouth?
Well congratulations, you're human. It's completely normal to struggle
with understanding some very complex concepts sometimes.
It's because your teacher is doing a very bad job at explaining a concept,
but often the concepts are just so complicated
that it's nearly impossible to immediately understand them
after hearing them for the first time.
In this video, I'm going to show you a strategy used by Richard Feynman,
one of the greatest physicists of all times, for solving very complex problems.
I'm also going to show you how I use this strategy for winning
a medal at the International Physics Olympiad.
Before we get started, make sure to subscribe to my channel down here for some more tips and tricks
and while you're there you can also hit the like button to push the YouTube algorithm.
Feynman's strategy can be applied to almost any kind of problems from simple
mathematics all the way up to differential geometry and even some business problems.
Feynman was a truly fascinating figure.
He won a Nobel Prize in Physics in 1965 for his work in quantum electrodynamics.
And little fun fact he walked these very corridors as a student at MIT.
But what made him so special compared to all the other great scientists was his unique personality
and incredible ability to understand complex concepts and solve difficult problems.
Surely Feynman was a very smart guy
but I'm very convinced that his intelligence alone played only a minor role in his success.
According to himself he only had an IQ of 124 which means that roughly
five percent of the world population is actually more intelligent than him.
So if Feynman could revolutionize Physics... this is kind of weird high gestures... revolutionize...
so if Feynman could revolutionize Physics with an IQ of 124
just by using clever problem solving strategies,
you can definitely do so much in your life no matter what your IQ is.
Before I dive into Feynman's problem solving strategy I
want to show you why having great problem solving skills
is probably the most useful skill you can acquire in your entire professional career.
It goes way beyond just solving math and physics problems.
The reason why some entrepreneurs and CEOs end up making billions of dollars
is because they managed to solve difficult problems which others were unable to solve.
So you gotta ask yourself — do you want to get paid just for the hours you invest like
a factory worker or do you want to get paid for your unique ability to solve difficult problems?
A factory worker can only make linear contributions, so if he does a twice as good of
a job he might double the revenue for his company. Therefore he might get a twice as large salary.
But problem solvers can make exponential contributions,
so if you become twice as good as solving problems you might significantly boost your
company's revenue putting almost no upper bound on your salary.
Therefore, if you want to become successful in your
career you should become a great problem solver.
Let's have a look at the problem that I made up. So we can solve it using the finance strategy.
It may be a bit too easy or too hard for you depending on your math skills,
but try to focus on the solving strategy rather than on the problem itself.
A drug test is 90 sensitive and 80 specific. Assuming 5 percent of the
total population consumes drugs, is a one-time random test a good way to identify drug users?
Feynman's problem solving strategy works roughly as follows.
Step number one is write down the problem that you want to solve.
Don't just copy it from the textbook, but try to rewrite it in a way that you can fully
understand it and then try thinking about what solution you're actually looking for.
For me, during Physics and Math competition that meant pulling out key information
converting to appropriate units and defining key terminology.
Don't feel embarrassed to spend a lot of time analyzing all of
the terminology and understanding every single word in the problem.
Understanding the problem can sometimes be the main step in solving the problem.
So once you're confident that you understood everything the solution might just be obvious
and if it is not obvious then just move on to step number two.
So let's apply step number one to our concrete problem. First of all,
what does it mean for a drug test to be 90 sensitive?
To be honest, I wasn't sure I had to look it up on Wikipedia.
It means that the true positive rate is 90. Next, what does 80 specific mean according to Wikipedia?
It means that for 100 people who do not use drugs,
we will have 80 correctly negative results and 20 falsely positive results.
If you still struggle to understand this
don't worry. Just have a look at Wikipedia and the visualization will explain everything.
Five percent of the population consuming drugs should be pretty clear,
but what does "good" mean in this context.
To understand this, let us think about what would it mean for a one-time random drug test to be bad.
Bad would probably mean that somebody who does not consume drugs gets randomly
tested and the test ends up being positive
meaning that he gets falsely accused of using drugs even though he doesn't.
So the word "good" in this context would mean that people rarely get
accused of using drugs even though they don't.
Put in mathematical terms the tests being very good means that the probability of someone
actually using drugs given that the test came back positive is very high or close to one.
So if you want to solve the problem we have to calculate this quantity
and check if it is close to one. This was step number one.
Instead of just staring at the problem and thinking about it
forever we already did fifty percent of the work by just analyzing it carefully.
Step number two according to Feynman is think really hard and
try to break up the problem into smaller sub-problems that you're able to solve.
Feynman's thinking process went way beyond just staring at the problem or a blank wall.
He would walk around, socialize, talk to his friends and colleagues
and explain everything he knew about the problems with them.
Feynman was even known for being a regular guest at a local strip
club close to Caltech where he worked after completing the Manhattan Project
and he would go there probably five times per week,
make drawings of naked girls and then he would also work on physics problems there.
While many researchers talk to each other about their scientific
research and therefore make a lot of progress,
Feynman's approach was really unique because he would talk to
random strangers who had no idea about his field.
Therefore, he had to express everything in layman's terms in a very simple way
and that helped him a lot to become a great scientist.
The ideal people to talk to are curious minds who will constantly
ask the why question, like a little child.
As humans are very curious beings,
we are constantly trying to figure out the why behind everything that we see.
One could even argue that this is what makes us different from all the other animals out there.
If you have to constantly explain all the problems that you're dealing with in a very simple manner
it will really help you to understand all the gaps in your knowledge and identify them very quickly.
The most interesting example of a brilliant idea that Feyman came up
with while explaining a simple concept is my own field of research quantum computing.
At some point during one of his physics lectures
at Caltech he was explaining why it was so hard to simulate molecules
and how interesting it would be to use quantum systems to simulate them more effectively.
This basic idea was the spark which ignited my entire field of quantum...
This basic idea was the spark which ignited my entire field of research.
If you would like to know more about quantum computing and my
PhD thesis you can check out my video over here
where I talk about all the fundamentals of quantum computing.
Some of the most difficult concepts that I ever had to understand in my life were
concepts in quantum mechanics and quantum electrodynamics.
Coincidentally many of these concepts were actually initially discovered by Richard Feynman.
The most difficult exam I had in my entire life was my quantum mechanics final exam.
Luckily I found two good friends who were roughly as knowledgeable as I am
so we spent the mornings trying to understand the concepts on our own
and in the afternoon we would come together, usually without understanding much,
and try to puzzle everything together until all of us would understand the difficult concepts.
At later points in my studies I wasn't lucky enough
to find someone to study with but it was okay.
I would just study on my own and I would try to explain all these
concepts either to my dog Milky or maybe to some of my plants.
If you are a university student, you could for example become a teaching assistant.
Just make sure that you will be actually teaching and not
just spending your time grading quizzes and exams.
I myself volunteered to host the Physics Olympiad preparations in my home country, Croatia.
This allowed me to rediscover Physics with some of
the smartest and most curious minds in the entire country.
Back to our drug testing problem. We know that for a random test to be good,
it means that the probability of someone actually using drugs
given that the test came back positive needs to be somewhere close to 1.
Let's have a look at this quantity. The probability of someone using drugs
given that the test came back positive.
So if this doesn't really look familiar to you this would be
the point where you would start talking to friends and colleagues
until somebody would eventually probably tell you that this looks a lot like the Bayes' theorem.
Obviously, I can't really demonstrate that process
over here, but let's just assume I got this information from someone.
Feel free to skip to this timestamp for step
number three or just continue watching. Solve the problem.
So first of all I'm going to start by writing down the Bayes' theorem in a
way that will be very easy to analyze and then compare it to quantities.
So let's get started.
So far I haven't really done anything new. But now when you
look at this you can very easily see in the first and second line
that A is equivalent to using drugs and B is just equivalent to the test being positive.
So now that we know what the quantities mean it should be
very easy to solve the rest of the problem.
All right, so now that we know exactly what is what. We can just look at the base formula
and try to figure out if we can find what the quantities on the right side are.
That is, P of B given a P of A and P of B. So first of all let's start with P of B given A.
But that is just the probability of the test being positive given that someone is using drugs.
So this quantity is just equal to the sensitivity that is the true positives which is 90
or 0.1...0.9 and next quantity is just P of A which is the probability of someone using drugs.
Well we already know that number. That's just five
percent of the people in total who are using drugs.
The last quantity that we have to figure out is P of B,
that is the probability of the test being positive.
So this may actually be the most tricky part of this whole problem to figure out because
it's asking us for the probability of a randomly selected person to be positive.
So if you can't really figure out what a number would be it's actually quite easy to analyze,
but just imagining a group of 1,000 people in total.
Out of these 1,000 people, 950 will not be using drugs and 50 will be using drugs.
Now all that is really left to do is count how many of these
tests are going to be positive for each of these two different groups.
So now instead of just looking at the 1,000 people as a one group
we can just split it up into 950 people who do not use drugs
and there we know how the test behaves
and 50 people who do use drugs and we also know how the test behaves for them.
So let's first look at the 950 people. We know that the false positive tests are going to be 20
so we just have to multiply 20 by 950
in order to get how many false positive tests we're going to have.
So there's a total of 190 false positive tests. For
the 50 people we also know how the test behaves.
Namely we know that for 90 of the people who actually do use drugs
the test is going to trigger and is going to tell us that it's positive.
So all that is now left to do is add up these numbers. That is 190 plus 45 which is 235.
So we know that out of the 1,000 tests that we made 235 of them turn positive.
In other words, 23.5 percent of the tests are positive, so P of B is 0.235.
That is basically it that we have to solve. Now we
just have to plug these numbers back into Bayes' theorem we are going to get a result
So overall the answer is roughly 19. In other words,
that means that only four out of five of the tests are actually correct.
Meaning that for every five people that get accused of using drugs only
one of them has actually been doing it and therefore the test is really bad.
This concludes step number two. Just to summarize step number one was
really understanding the problem and analyzing every aspect of it
and step number two was talking to other people and explaining to them everything
you know about the problem so they can challenge you in everything you say.
Also you should always break down the problem into sub-problems. Step number three
according to Feynman is write down your solution.
This may sound a bit silly and I personally haven't written
down many solutions for many years and I deeply regret it.
As I explained in my video about the best study methods there are
two parts to learning something memorization and understanding.
You often make the mistake thinking that for example Geography your History is all
about memorization and Math and Physics is just about understanding something
but this is completely wrong. Understanding a complex concept
may be a great mind exercise but in the end of the day if you do not remember
what you understood at some point in the past you will not be able to use that skill in the future.
I personally learned so many advanced mathematical tools in university and I really
understood them during my exam but then after the exam I would never really write them down
and nowadays I really regret that I actually forgot most of them so I can't really use them.
The active recall and space repetition techniques allow you to memorize things for life.
So after watching this make sure to check out my video
on space repetition and active recall techniques.
The solution to my struggles which drastically changed my life in so many ways came from my mom.
One day in 10th grade she came to me and told me about the software called Anki.
Anki is the only software for which I would seriously say that it changed my life.
This concludes step number three. In addition to Feynman's principles for solving problems,
I'm now going to give you a few tips and tricks which I use throughout my life.
One of the major reasons why a lot of people struggle solving
complicated problems especially if they're under time pressure
is because they don't manage to stay calm and just follow the problem-solving procedure.
Oh my god okay it's happening everybody
stay calm what's the procedure everyone what's the procedure.
At the International Physics Olympiad I would sometimes be confronted with
incredibly complicated problems that took several pages just to explain.
But instead of panicking and just staring these problems I would just
calmly follow Feynman's procedure for solving problems and after some time
I would end up with a solution. If you're still having difficulty solving certain problems,
at least in mathematics science and maybe engineering, you can apply the following tricks.
If you struggle solving some kind of analytical problem or a problem that
has very messy numbers you could for example replace all of them with one
and try to visualize the entire problem. Some problems are just too complicated
because they have so many variables so by setting some of them equal to zero
and solving the problem first you can understand it and then you can
always come back and solve the original problem.
Or instead of making variables equal to zero you can simply remove some of the
information from the problem and then write it down in a more simple way.
If you don't know how to approach a certain problem maybe you solved
a similar problem in the past so first have a look at that figure out how you
solve that and then maybe the solution will become obvious.
Jeff Bezos once wanted to become a theoretical physicist.
That's why he was studying at Princeton and when he was really stuck with a problem for many hours,
he then just walked up to a friend and was like hey I don't really know how to solve
that can you help me and his friend just looked
at the problem he could tell him the solution on the spot.
When Bezos asked him how exactly he did that his friend simply replied oh
yeah it's a bit similar to another problem that he saw in class and
therefore the solution was obvious and Jeff Bezos was so discouraged by the fact that
he simply couldn't comprehend this that eventually he gave up
on doing Physics he started Amazon. Also if your first attempt to solve a problem didn't work
don't try again the same way try thinking about other ways
you could approach this problem. Quantum mechanics itself was probably the silliest possible solution
to explain all the inconsistencies in Physics in the early 20th century
but yet it turned out to be true. These were my
strategies for understanding and solving complex problems.
If you want to learn more about how to understand math
intuitively you can check out my video over here.
If you would like to learn about study methods and
memorization methods you can check out my video over here.
And if you're just curious about my PhD research in Quantum Artificial Intelligence
check out my video over here.
Thanks for watching don't forget to like the video and subscribe to
my channel and I'll see you next time. Take care.